Solve for $x$ and $y$ using elimination. ${2x-2y = -18}$ ${3x+6y = 63}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ ${6x-6y = -54}$ $3x+6y = 63$ Add the top and bottom equations together. $9x = 9$ $\dfrac{9x}{{9}} = \dfrac{9}{{9}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {2x-2y = -18}\thinspace$ to find $y$ ${2}{(1)}{ - 2y = -18}$ $2-2y = -18$ $2{-2} - 2y = -18{-2}$ $-2y = -20$ $\dfrac{-2y}{{-2}} = \dfrac{-20}{{-2}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {3x+6y = 63}\thinspace$ and get the same answer for $y$ : ${3}{(1)}{ + 6y = 63}$ ${y = 10}$